"calm down" or "take it easy"

sometimes it is like calm down, and it also can describe "think over" for example, if your friends are arguing, you can say 冷静冷静, then it means calm down. if you meet a ticklish matter in your work, you can't settle it now, maybe you will talk to yourself 冷静冷静，then it means calm down and let me think it over.

Quiet, peaceful mood to

Yes. it's for casual chat, notice that it's repeat of "冷静" which already means calm down or take it easy. You can also say "冷静一下" or "冷静点".

it's for casual chat~just means calm down or control yourself when others are humorsome or excited.it's used for joke and fun not for the situation in which someone really gets angry.